powerindexR (version 1.6)

pi.shapley: Power based on the Shapley-Shubik index.

Description

This function determines the distribution of the power based on the Shapley-Shubik index and the Owen value.

Usage

pi.shapley(quota, weights, partition = NULL)

Value

Shapley value

The Shapley value, if partition=NULL.

Owen value

The Owen value, if partition!=NULL.

Arguments

quota

Numerical value that represents the majority in a given voting.

weights

Numerical vector of dimension \(n\) that indicates the weights of \(n\) agents in a given voting.

partition

Numerical vector that indicates the partition of voters. Each component indicates the element of the partition to which such voter belongs. If it is not NULL, it provides the distribution of the power based on the Owen value.

Author

Livino M. Armijos-Toro, Jose M. Alonso-Meijide, Manuel A. Mosquera, Alejandro Saavedra-Nieves.

References

Alonso-Meijide, J. M., & Bowles, C. (2005). Generating functions for coalitional power indices: An application to the IMF. Annals of Operations Research, 137, 21-44.

Lucas, W. F. (1983). Measuring power in weighted voting systems (pp. 183-238). Springer New York.

Examples

# Example Shapley value
weights<-c(137,85,71,32,9,8,5,2,1) 
quota<-176
pi.shapley(quota,weights)

# Example Owen value
quota<-30
weights<-c(28, 16, 5, 4, 3, 3)
# Partition={{1},{2,4,6},{3,5}}
pi.shapley(quota,weights,partition=c(1,2,3,2,3,2))